A347434 E.g.f.: exp( exp(x) * (exp(x) - 1 - x - x^2 / 2) ).

1, 0, 0, 1, 5, 16, 52, 274, 1990, 14354, 99704, 730225, 6061013, 56151330, 551040830, 5597109717, 59324775741, 664973687438, 7891158217876, 98253448977890, 1273082291906394, 17124091446383666, 239333235895599762, 3476600533730954761, 52394273274018321421

Offset

0,5

Comments

Exponential transform of A002662.

Links

Table of n, a(n) for n=0..24.

Formula

a(0) = 1; a(n) = Sum_{k=1..n} binomial(n-1,k-1) * A002662(k) * a(n-k).

Maple

a:= proc(n) option remember; `if`(n=0, 1, add(
      a(n-j)*binomial(n-1, j-1)*(2^j-j*(j+1)/2-1), j=1..n))
    end:
seq(a(n), n=0..24);  # Alois P. Heinz, Sep 02 2021

Mathematica

nmax = 24; CoefficientList[Series[Exp[Exp[x] (Exp[x] - 1 - x - x^2/2)], {x, 0, nmax}], x] Range[0, nmax]!
a[0] = 1; a[n_] := a[n] = Sum[Binomial[n - 1, k - 1] (2^k - 1 - k (k + 1)/2) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 24}]

Crossrefs

Cf. A002662, A006505, A055882, A143405, A347432, A347435.

Sequence in context: A371437 A274492 A147536 * A173871 A108300 A041469

Adjacent sequences: A347431 A347432 A347433 * A347435 A347436 A347437

Keyword

nonn

Author

Ilya Gutkovskiy, Sep 02 2021

Status

approved